Approximate coalgebra homomorphisms and approximate solutions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F20%3A00346315" target="_blank" >RIV/68407700:21230/20:00346315 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/978-3-030-57201-3_2" target="_blank" >https://doi.org/10.1007/978-3-030-57201-3_2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-030-57201-3_2" target="_blank" >10.1007/978-3-030-57201-3_2</a>

Result language
angličtina
Original language name
Approximate coalgebra homomorphisms and approximate solutions
Original language description
Terminal coalgebras ν F of finitary endofunctors F on categories called strongly lfp are proved to carry a canonical ultrametric on their underlying sets. The subspace formed by the initial algebra μ F has the property that for every coalgebra A we obtain its unique homomorphism into ν F as a limit of a Cauchy sequence of morphisms into μ F called approximate homomorphisms. The concept of a strongly lfp category includes categories of sets, posets, vector spaces, boolean algebras, and many others. For the free completely iterative algebra Ψ B on a pointed object B we analogously present a canonical ultrametric on its underlying set. The subspace formed by the free algebra φ B on B has the property that for every recursive equation in Ψ B we obtain the unique solution as a limit of a Cauchy sequence of morphisms into φ B called approximate solutions. A completely analogous result holds for the free iterative algebra RB on B.
Czech name
—
Czech description
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Project
<a href="/en/project/GA19-00902S" target="_blank" >GA19-00902S: Injectivity and Monads in Algebra and Topology</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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